Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
inline ld get(ld h, ld x0, ld x1) { return 0.5 * (x1 * x1 / h - x0 * x0 / h); }
int main(int argc, char **argv) {
  ios::sync_with_stdio(false);
  cin.tie(0);
  srand(time(0));
  int n;
  ld h;
  cin >> n >> h;
  ld sum = (0.5 * h) / n;
  ld prev = 0;
  for (int i = 0; i < n - 1; ++i) {
    ld l = prev + 0.000000001, r = h, mid;
    while (r - l > 0.000000001) {
      mid = l + (r - l) / 2.0;
      if (get(h, prev, mid) > sum) {
        r = mid;
      } else {
        l = mid;
      }
    }
    cout << setprecision(20) << fixed << l << endl;
    prev = l;
  }
}